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6x^2-20x-27=0
a = 6; b = -20; c = -27;
Δ = b2-4ac
Δ = -202-4·6·(-27)
Δ = 1048
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1048}=\sqrt{4*262}=\sqrt{4}*\sqrt{262}=2\sqrt{262}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-2\sqrt{262}}{2*6}=\frac{20-2\sqrt{262}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+2\sqrt{262}}{2*6}=\frac{20+2\sqrt{262}}{12} $
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